Answer:
[-4, 7]
Step-by-step explanation:
the ‘( )’ implies not inclusive of, whereas ‘[ ]’ implies inclusive of
Therefore, that is the answer,
things to note in general:
- the values should go in ascending order from left to right
e.g (x, x+1) where x is a real number
- if you want to connect two intervals, you would use U or union
e.g (2, 3)U(4,5]
- also, from the previous answer, it is valid if you use set notation such as ‘(x, y]’ and ‘[x, y)’ where x < y, x and y are real
These are equivalent in ‘inequality notation’ as, if we consider p to be in these intervals:
x < p <= y
And
x <= p < y
respectively,
- If we have, say
(x,y]U[y,z) where x, y and z are real, x<y<z
You could combine it to form
(x,z)
Another example would be:
let p be in this domain
[x,x]
Which is equivalent to saying,
x<=p<=x
But by the squeeze theorem, we get that p = x
-notating asymptotes:
for asymptotes that graphs don’t exist beyond it, say, the range of y = e^x
it can be expressed as
(0, inf)
note that infinity is not, as I know of it, considered an asymptote, but we just can’t get to it exactly.
You can define infinity as, paraphrasing here ‘the number of numbers’
we actually can’t assign a value to that, as there will be a number at least 1 greater than any number you specify, but I digress,
The asymptote here is really y = 0 as when x is negative, we can reciprocate to get a fraction, which has 1 in the numerator.
But we all know that a fraction with a constant numerator cannot equal 0 for any denominator in the set of real numbers
Therefore, the asymptote is y = 0
Applying the same logic,
for asymptotes that graphs do exist beyond them, say, y = 1/x
The range is
(-inf, 0)U(0, inf)
where the asymptote is again y = 0
